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Potential scattering as opposed to scattering associated with independent particles in the S-matrix theory of strong interactions

Chew, Geoffrey F. and Frautschi, Steven C. (1961) Potential scattering as opposed to scattering associated with independent particles in the S-matrix theory of strong interactions. Physical Review, 124 (1). pp. 264-268. ISSN 0031-899X. doi:10.1103/PhysRev.124.264.

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A definition of a relativistic generalized potential is given, suitable at arbitrary energies for a pair of particles whose elastic scattering amplitude satisfies the Mandelstam representation. It is shown that the generalized potential plays a role in the dynamics analogous to that of the ordinary nonrelativistic potential in a Schrodinger equation and determines the scattering to the same extent. Below the threshold for inelastic processes the generalized potential is real and its energy dependence in the elastic region is expected for certain particle combinations (such as the nucleon-nucleon) to be weak. In such cases one may uniquely define, for use in the Schrodinger equation, an energy-independent ordinary potential that coincides with the potential of Charap and Fubini (Abstr. 1960A01252). In general, when the potential is complex and energy-dependent the dynamical problem involves iteration of an integral equation deduced by Mandelstam (Abstr. 1959A04941). The generalized potential may be decomposed according to range and it is shown that keeping only the long-and medium-range parts, corresponding to transfer of one or two particles, is almost equivalent to the "strip approximation." Finally, a general definition is given of "pure potential scattering" as opposed to scattering associated with "independent" particles, either stable or unstable, and a variety of experimental situations are discussed with respect to this distinction, which is shown to be susceptible to experimental test.

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Additional Information:© 1961 The American Physical Society. Received 11 May 1961; revised 14 June 1961. This work was performed under the auspices of the U.S. Atomic Energy Commission.
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Atomic Energy CommissionUNSPECIFIED
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12454
Deposited By: Tony Diaz
Deposited On:11 Dec 2008 18:34
Last Modified:08 Nov 2021 22:28

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